Deine Mutter (always with capitals)
are NOT swear words unless you add something to it like:
Deine Mutter ist eine Hure.
(Your mother is a whore)
which is a serious insult
Nowadays "Deine Mutter" can be used as a swear word on its own and will be understood by any German! May also be used as a German equivalent to "In your face!" or "you are talking bullshit!"

"fick dich" (singular) or "fickt euch" (plural) means fuck you and is used the same way "fuck you" is used in English, mostly to express that someone is being an asshole/annoys you. Also can be used as an equivalent for "bite me", but it's more offensive.

shut up and doen't include the word "fuck". it merely means stop talking in a somewhat deameaning and insulting way. less insulting but still impolite would be "halt(en) sie/du den mund". it has nothing to do with with a way of eating like an animal.

PracticalUsage

the same meaning: "halts maul!"
Germans hate being associated with animals, and this means "stop eating like an animal" but translated loosely into "shut the fuck up." Use with anger and fists raised.

"She looked okay when we were in the bar, but when I woke up the next morning it turned out she was a complete minger. On fire and put out with a shovel, that sort of thing."
NB: This is from the UK, not Germany.

Used to refer to someone who always has constant complaints about everything he/she encounters; someone who complains about everything; for example bad service, bad food, the weather is too hot or cold, and so on.....also known as the perpetual "fusspot" or constantly picky person

This insult is used in a similar way as the English "moron" It describes a person that is inferior to others, such as someone who is constantly bullied. With "Wichser", "Hurensohn" and "Spasst" one of the most commonly and widely used insults.

"Listen here, Scheisskopf, the gravy goes on the potatoes in one scoop....any more and it's comin' outta your check."
If you said Scheisskopf to any german they would just simply laugh at you, Dummkopf is a softer and friendlier word for being idiotic.